Connect the diagonal lines of the square and divide the windmill into eight parts.

Only look at the part within 1 semicircle: including 1 isosceles right triangle with the side of the square as the hypotenuse+the area of two arcs formed by triangle and semicircle (this area = 1/4* windmill area).

Namely: 1/4* windmill area = semicircle area-isosceles right triangle with 4 as hypotenuse.

=0.5*3. 14*2*2-0.5*4*2

=6.28-4

=2.28

So the windmill area =2.28*4=9. 12.